PRIMALITY PROOF for Wagstaff numbers!

[retina]

Originally Posted by nobody

W170141183460469231731687303715884105727 is prime!

[R.D. Silverman]

Originally Posted by nobody

We are good for all p being prime numbers from 3 to 374321 inclusive, 986191 and 170141183460469231731687303715884105727 now.

Wp = (2^p + 1) / 3 (set to display last 25 digits of Wp)

W3 is prime! W3 = 3
W5 is prime! W5 = 11
W7 is prime! W7 = 43
W11 is prime! W11 = 683
W13 is prime! W13 = 2731
W17 is prime! W17 = 43691
W19 is prime! W19 = 174763
W23 is prime! W23 = 2796203
W31 is prime! W31 = 715827883
W43 is prime! W43 = 2932031007403
W61 is prime! W61 = 768614336404564651
W79 is prime! W79 = 201487636602438195784363
W101 is prime! W101 = 400152152934331135470251
W127 is prime! W127 = 6410577229101238628035243
W167 is prime! W167 = 2862561408838653121833643
W191 is prime! W191 = 1069350392574077339085483
W199 is prime! W199 = 3753700498963798805883563
W313 is prime! W313 = 3869220418099018130434731
W347 is prime! W347 = 7002917439712921903606443
W701 is prime! W701 = 9548478180862167823854251
W1709 is prime! W1709 = 6975212036857299070528171
W2617 is prime! W2617 = 2079499645847933435947691
W3539 is prime! W3539 = 3732972086304686486497963
W5807 is prime! W5807 = 9459748642466686663568043
W10501 is prime! W10501 = 2813453630340431558126251
W10691 is prime! W10691 = 4601633276209259644365483
W11279 is prime! W11279 = 7387805213081084271176363
W12391 is prime! W12391 = 8359843183967789680077483
W14479 is prime! W14479 = 3689259682678801865288363
W42737 is prime! W42737 = 1349264841566953606392491
W83339 is prime! W83339 = 359384937298240746465963
W95369 is prime! W95369 = 4033674797238688961702571
W117239 is prime! W117239 = 7907571738678737515489963
W127031 is prime! W127031 = 2870699169405437930547883
W138937 is prime! W138937 = 3537961127544933256440491
W141079 is prime! W141079 = 7199272469066889206344363
W267017 is prime! W267017 = 6517089403234044231723691
W269987 is prime! W269987 = 6555348340619494443100843
W374321 is prime! W374321 = 6129114830908904702651051
W986191 is prime! W986191 = 5700800218839434692045483
W170141183460469231731687303715884105727 is prime!
W170141183460469231731687303715884105727 = 1871913029119479164611243

Did you forget to take your lithium?

[akruppa]

nobody = Terrence Law.

Alex

[R.D. Silverman]

Originally Posted by akruppa

nobody = Terrence Law.

Alex

It is inherently dishonest of him to hide behind a pseudonym. Can something
be done? He already has a registered name.

[ewmayer]

Originally Posted by R.D. Silverman

It is inherently dishonest of him to hide behind a pseudonym. Can something
be done? He already has a registered name.

Something has been done - he can of course attempt to create new aliases, but that would risk him getting himself a permanent IP-level ban. (Which I'm sure some would welcome, but since general crankery is not against the rules here, we require actual violations of forum rules).

[Jeff Gilchrist]

While I realize this doesn't prove the conjecture, back in October I created a GMP program that implements the conjecture for Wagstaff primes and ran it for prime exponents 3 up to 350000 just to see if there were any counter-examples. With all the misinformation posted by Terrence Law and him copying and pasting some of my results, I wanted to post my last findings along with the source code of the program in case anyone else wants to play around with it.

The test results up to 350000 find all the primes or probable primes that have so far been discovered.

Wagstaff Prime Prover v1.1 (using Anton Vrba conjecture)
by: Jeff Gilchrist [http://gilchrist.ca/jeff]
Oct. 24, 2008

# Note: This is only a conjecture, and has not been proven! #
#  See: http://www.mersenneforum.org/showthread.php?t=10737 #

Wp = (2^q + 1) / 3      (set to display last 25 digits of Wp)

Checking prime q values from 3 to 350000...
W3 is prime!  W3 = 3 (1 digits)
W5 is prime!  W5 = 11 (2 digits)
W7 is prime!  W7 = 43 (2 digits)
W11 is prime!  W11 = 683 (4 digits)
W13 is prime!  W13 = 2731 (4 digits)
W17 is prime!  W17 = 43691 (5 digits)
W19 is prime!  W19 = 174763 (6 digits)
W23 is prime!  W23 = 2796203 (7 digits)
W31 is prime!  W31 = 715827883 (10 digits)
W43 is prime!  W43 = 2932031007403 (13 digits)
W61 is prime!  W61 = 768614336404564651 (19 digits)
W79 is prime!  W79 = 201487636602438195784363 (24 digits)
W101 is prime!  W101 = ...400152152934331135470251 (31 digits)
W127 is prime!  W127 = ...6410577229101238628035243 (38 digits)
W167 is prime!  W167 = ...2862561408838653121833643 (50 digits)
W191 is prime!  W191 = ...1069350392574077339085483 (58 digits)
W199 is prime!  W199 = ...3753700498963798805883563 (60 digits)
W313 is prime!  W313 = ...3869220418099018130434731 (94 digits)
W347 is prime!  W347 = ...7002917439712921903606443 (105 digits)
W701 is prime!  W701 = ...9548478180862167823854251 (211 digits)
W1709 is prime!  W1709 = ...6975212036857299070528171 (515 digits)
W2617 is prime!  W2617 = ...2079499645847933435947691 (788 digits)
W3539 is prime!  W3539 = ...3732972086304686486497963 (1066 digits)
W5807 is prime!  W5807 = ...9459748642466686663568043 (1748 digits)
W10501 is prime!  W10501 = ...2813453630340431558126251 (3161 digits)
W10691 is prime!  W10691 = ...4601633276209259644365483 (3219 digits)
W11279 is prime!  W11279 = ...7387805213081084271176363 (3396 digits)
W12391 is prime!  W12391 = ...8359843183967789680077483 (3730 digits)
W14479 is prime!  W14479 = ...3689259682678801865288363 (4359 digits)
W42737 is prime!  W42737 = ...1349264841566953606392491 (12865 digits)
W83339 is prime!  W83339 = ...359384937298240746465963 (25088 digits)
W95369 is prime!  W95369 = ...4033674797238688961702571 (28709 digits)
W117239 is prime!  W117239 = ...7907571738678737515489963 (35293 digits)
W127031 is prime!  W127031 = ...2870699169405437930547883 (38240 digits)
W138937 is prime!  W138937 = ...3537961127544933256440491 (41824 digits)
W141079 is prime!  W141079 = ...7199272469066889206344363 (42469 digits)
W267017 is prime!  W267017 = ...6517089403234044231723691 (80380 digits)
W269987 is prime!  W269987 = ...6555348340619494443100843 (81274 digits)
Finished! Checked prime q values to: 349981

Attached is the C source code that you need to link with GMP.

Jeff.

[Uncwilly]

Originally Posted by akruppa

nobody = Terrence Law.

Is that better phrased:
Terrence Law = nobody
?

[akruppa]

If his name were Terence Hill, yes. Maybe we can cross-breed him with DJH?

Alex

[henryzz]

Originally Posted by AntonVrba

For Fermets I have not studied.

More intersting is that one can also prove

2^q - 5 , s0 = 6 , s2 = sq
2^q - 3 , s0 = 4 , s2 = sq
2^q - 1 , s0 = (4p-10)/3 , s1=sq ; This is w=-3-1/3
2^q + 3 , s0 = 6 , s2 = sq
2^q + 4 , s0 = 4 , s2 = sq
2^q + 7 , s0 = 5 , s3 = sq

I need to investigate the +- Wq

would these tests be better faster than rabin-miller?